1. Field of the Invention
This invention relates to obtaining data for use in determining whether a linear system meets design criteria.
2. Description of the Prior Art
The output of a linear system is the product of the input to the system and the system transfer characteristic. With this in mind systems are constructed to exhibit -- as closely as possible -- characteristics which result in desired outputs for particular inputs. Loading coils, for example, are added in telephone transmission lines to modify the lines so as to improve the quality of the output.
Notwithstanding attempts to have systems exhibit particular transfer characteristics, such characteristics are not always present because of faulty construction, faulty components, or damage while in shipping, installation or use. It is therefore often necessary to obtain data for use in determining whether the desired characteristics are present.
Data which would be helpful are system poles and zeros. Detailed discussions with respect to poles and zeros are presented in standard textbooks. In brief, system poles and zeros are terms associated with transfer characteristics expressed as Laplace transform functions. In particular, such functions contain the Laplace operator s which represents a complex frequency variable. The values of the operator s which cause the value of a function to go to infinity are called poles. On the other hand the values of the operator s which cause the value of a function to go to zero are called zeros.
Complex frequency variables are, of course, not available in real life and consequently system poles and zeros cannot be specifically identified by testing. However, if the resistive components of a system are relatively small with respect to the reactive components, then poles and zeros can be identified in an approximate manner by testing the system for maximum and minimum impedance or admittance (i.e., immittance) values as a function of frequency. Data so obtained for transmission lines with loading coils, for example, have been found adequate to determine if the desired loading is present.